Abstract: The evaluation of the joint probability density function from the joint moment generating function involves an M-dimensional inverse laplace transform. The analytic and numerical difficulty of performing this task for large values of M prompts consideration of an approximate technique such as the saddlepoint method. Advantage can be taken of the fact that the joint probability density function is real and positive, to show that the dominant saddlepoint in the original region of analyticity of the joint moment generating function is on the real axes. Furthermore, inside this region of analyticity, the integrand of the inverse Laplace transform has a positive-definite Hessian matrix on these real axes, indicating a single minimum for the saddlepoint location, when it exists. These properties serve to reduce the numerical effort required to locate the dominant M-dimensional saddlepoint. Examples of some statistical problems where this issue is of importance are included.
| Limitations: |
 APPROVED FOR PUBLIC RELEASE |
| Pages: |
74 |
| Report Date: |
15 JUL 2002 |
| Report Number: |
A054504 |
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